Let 1, 2, 3, and 4 are vertices of the square (counterclockwise order) and e_1, e_2, e_3, and e_4 are edges between these vertices.

Let G_x be the stabilizer of x. Then,

G_1 = {e, (2,4) }, G_2 = {e, (1,3)}, ....

G_e1 = {e, (1,2)(3,4)}, G_e2 = {e, (14)(23)}, ....

The stabilizer elements for the above action are identity, 180 degree rotation, diagonal flip, and 180 degree rotation after diagonal flip. What are these elements in D_4?(b) G acts on the set of two elements consisting of the diagonal lines. What is the stabilizer of a diagonal?